Virtual coupling uses wireless communication instead of mechanical coupling to ensure that trains are easily reconnected or disconnected. This technology can shorten the interval time between trains, give full play to the carrying capacity of lines, and improve the service level of urban rail transit. This paper optimizes the train operation plan with full-length and short-turn routes of virtual coupling trains by establishing a two-level optimization model. The upper model is used to minimize passenger travel time and enterprise operation cost, and the lower model to optimize the equilibrium of train load rate on short-turn routes. Meanwhile, a method based on the genetic algorithm is designed to solve the model. A case study of the Metro Line M has been carried out. The results can verify the efficiency and feasibility of the proposed method. The full-length and short-turn routes of virtual coupling trains can effectively reduce passenger travel time, enterprise operating cost and the number of vehicles, and improve the average load factor of the trains. Finally, sensitivity analyses are performed using three parameters which include departure frequency of the full-length train and short-turn train, starting and terminal station of short-turn route, and number of marshalled vehicles of the full-length train and short-turn train.

It has been proven that developing urban rail transit (URT) is the key to solving the traffic problems in big cities, and transport efficiency is essential for scientific line planning and construction, operation management and sustainable development of urban rail transit. This paper focuses on the transport efficiency of the URT network and adopts shadow efficiency theory creatively to combine factors of passengers, capacity, and efficiency effectively. A quantitative calculation method of system utility based on “double time penalty” is proposed. According to the characteristics of Beijing URT, this paper puts forward a single optimization strategy and combinatorial optimization strategy and analyzes the results with DEA. The simulation of Beijing subway network proves the availability of the method and its optimization effects.

The advancement of virtual coupling technology in urban rail transit has facilitated the online coupling and decoupling of trains, enabling a range of flexible transportation configurations, including various route types and adjustable formations. This study targets the fluctuating passenger demands on urban rail lines, aiming to minimize both passenger travel and operational costs. The model integrates constraints associated with virtual coupling, train operations, rolling stock circulation, and the interaction between virtually coupled trains and passenger arrivals. New decision variables are introduced to depict the train formation state under virtual coupling scenarios. An integrated optimization model for train diagrams and rolling stock circulation under virtual coupling conditions is developed, employing a genetic-simulated annealing algorithm informed by train operation simulations. A case study on an urban rail line during the morning peak examines the optimization of train diagrams for full-length and short-turn routes. Findings confirm that virtual coupling technology effectively adapts to lines with uneven passenger flow distribution, significantly enhancing the match between supply and demand, equalizing spatial and temporal traffic variations, and harmonizing the quality of passenger services with operational efficiency.